Using conventional ordinary least squares, we estimated the 50-state econometric model on pooled time series and cross-section data on state and local spending for the 24 years from 1977 to 2000. We conducted standard tests for auto-correlation of residuals, which sometimes constitutes an issue for time series analysis.19

The model and its estimates had two general purposes. First, the model estimates allowed us to assess the magnitude and statistical significance of variables of interest, such as state fiscal capacity as measured by per capita personal income, federal grants, and other determinants of state and local spending. Second, the model estimated state effects used in the comparisons among rich and poor states in general and among the six poor states selected for further analysis. We report an overview of the results in the text of this report. More detailed estimation results appear in Appendix A.

We estimated a number of models,20 but for purposes of this discussion we will focus on a single preferred model in which we allow for flypaper effects by including both state personal income and federal grants as separate variables, and we attempt to measure state and local needs through the poverty, unemployment, and population density variables. Both state and year dummies are included.

Below, we present the results, first for the regressions estimated over all states and then for the regressions estimated separately for each quartile defined by the historical average of real PCPI.

Exhibit III-10 displays the regression results for the five regressions with dependent variables defined as respective categories of per capita state and local spending (CA - cash assistance, M - Medicaid, NSS - non-health social services, PH - public hospitals, and non-social welfare - NW) for all states.21 Below the estimated coefficients, t-statistics appear in parentheses. A t-value greater than approximately 1.96 indicates statistical significance at the .05 level, and a t-value greater than approximately 2.44 indicates statistical significance at the .01 level.

As shown in Exhibit III-10, the linear effects of per capita personal income on per capita social welfare spending after we control for federal grants and need are positive, and statistically significant for Medicaid and non-health social services. However, the effects are negative and statistically significant for cash assistance and statistically insignificant for public hospital spending.22 The impact of per capita personal income on per capita non-social welfare spending is larger, but we expected this outcome because non-social welfare spending is much larger than the individual components of social welfare spending.23

When we examine the effects of federal grants on the components of social welfare spending for all states in Exhibit III-10, we find, unsurprisingly, that grants for non-social welfare exert weak and statistically insignificant effects on cash assistance and Medicaid spending, but such grants exert much stronger and statistically significant effects on non-health social services and public hospital spending. This result might constitute evidence of a positive income effect of non-social welfare grants24 on the latter two categories of non-health social services and hospital spending. The federal grants for social welfare have strong, positive, and generally statistically significant effects on spending for cash assistance, Medicaid, and public hospitals. The effect of federal grants on Medicaid is particularly strong, indicating the attractiveness to the states in matching federal Medicaid dollars.

Exhibit III-10 also shows the results for the three main indicators of need for social welfare spending (i.e., poverty per capita, unemployment per capita, and population density) for all states. The negative signs on the poverty variable seem surprising and difficult to explain. Possibly the measures of fiscal capacity and federal grants are insufficient to capture the state's perceived resources and poverty proxies for available resources (in a negative direction). Also, high poverty states might resist spending because of an omitted unobserved variable correlated with poverty. The poverty variable was statistically significant and negative only for Medicaid and public hospital spending.

Unemployment per capita had the expected positive sign for all categories of social welfare spending except non-health social services, and the effect was statistically significant for cash assistance, Medicaid, and public hospitals. Population density was statistically significant for all categories of social welfare spending, including public hospitals, but was positive for cash assistance and negative for Medicaid, non-health social services, and public hospitals.

Exhibit III-11 shows results for the same regression model estimated separately for each of the 4 quartiles defined by mean real per capita personal income. Below, we summarize the general findings from this analysis by quartile and spending category for the explanatory variables of greatest interest: (1) fiscal capacity, (2) federal grants, (3) need variables, (4) state unemployment rates, and (5) state effects.

To confirm that the effects estimated for the unemployment per capita variable were truly state labor market effects and to get a better sense of how spending changed in response to unemployment changes alone, we estimated simple linear relationships between spending per capita in each category and the state unemployment rate with and without per capita personal income as an additional explanatory variable. In the regressions of per capita spending on the state unemployment rate alone (but including state effect dummies) for all states, as shown in Exhibit III-12, spending for cash assistance and public hospitals was positively related to unemployment, in other words an anti-cyclical effect,28 but spending on Medicaid and other social welfare was negatively related to unemployment, a pro-cyclical effect.

Exhibit III-12.
Coefficient Estimates Showing Impact of State Unemployment Rate Without Year Dummies

To see how much of the effect of unemployment was operating through the per capita personal income variable, we included per capita personal income in the regression. These results can be seen also in Exhibit III-12. Over all states, the unemployment rate exerted a positive effect on spending for all categories of social welfare spending, and the effect was statistically significant for all categories except non-health social services. Thus, the presence of the per capita personal income variable has eliminated the negative effect for Medicaid and non-health social services spending observed in the regression on the unemployment rate alone. The fact that unemployment and personal income are negatively correlated suggests the negative effects observed in Exhibit III-12 are due to the absence of a control for income. Across all states, then, unemployment seems to do an effective job of picking up positive need effects on spending, except for other non-health social welfare, with personal income held constant. This finding is generally consistent with the results reported in Exhibit III-10 with other explanatory factors (e.g., poverty, population density, federal grants, and year dummy variables) in addition to personal income included in the regression.

One result of the 50-state model was the estimation of unexplained variance in spending across different states. These state effects were estimated intercepts or constant terms for each of the states in the econometric models. They may be interpreted as general dispositions of states-averaged across the entire period, 1977-2000-to support certain types of spending after controlling for the linear effects of fiscal capacity, social needs, federal grants, and population density.29

In their original form, the state intercepts, or effects, were difficult to interpret. To make them easier to understand, we standardized them with respect to the mean and standard deviation of the state effects. That is, for each set of estimated state effects-one set of 50 for each dependent variable, such as cash assistance or Medicaid-the mean of the 50 state effects was set at zero and the standard deviation was set at 100. Thus, if a state's effect for Medicaid was 2 standard deviations above the mean of the 50 state effects that particular effect was scored as 200. If the state's effect for cash assistance was 1/4 of a standard deviation below the mean for all states, then that effect was scored -25.

Exhibit III-13 shows the standardized versions of the estimated state effects for all of the states. The larger and more positive the number, the greater the tendency of the state to spend on that particular category of public function over the entire time period, 1977-2000, after controlling for the linear effects of the other independent variables, including per capita personal income, per capita grants, and the various need variables. For example, even after controlling for these factors, Alaska shows a strong additional propensity to spend on cash assistance and non-social welfare and a tendency to spend less on Medicaid and public hospitals relative to other states. New York and Minnesota, however, show additional propensities (again, compared to other states) to spend more than predicted by the econometric model on all social programs.

Despite the good fit of the models to the data, these state effects show variation in their spending on different types of social programs. For example, the difference between the 25th and 75th percentiles in the state effect estimates for cash assistance is $49 per capita, a large amount compared to the mean per capita spending for all states (averaged over all years, 1977-2000) of $82.

Cash Assistance

Medicaid

Non-heath Social Services

Public Hospitals

Non-social Welfare

Exhibit III-13.
Overall State Effects for Regression Model

Quartile 1

Alaska

273

-171

19

-190

611

California

275

-47

-2

30

-18

Connecticut

123

92

-14

52

-106

Delaware

-24

-141

75

-96

9

Hawaii

207

-39

-122

-57

33

Illinois

102

1

14

-52

-62

Maryland

27

85

-51

-48

-63

Massachusetts

79

292

152

48

-64

Nevada

-59

-98

-140

64

-10

New Hampshire

-10

77

115

-134

-61

New Jersey

-43

190

117

39

-95

New York

189

110

309

133

38

Quartile 2

Colorado

-3

-109

-16

-30

-3

Florida

-64

12

-107

55

-39

Kansas

-3

-47

-93

23

-9

Michigan

147

-79

122

8

-27

Minnesota

125

169

129

46

18

Ohio

44

48

45

-23

-61

Oregon

-10

-167

-19

-63

35

Pennsylvania

72

-43

232

-74

-56

Rhode Island

4

260

208

1

-70

Virginia

32

-25

-112

-1

-51

Washington

88

-58

-49

-34

54

Wisconsin

46

107

94

-65

-1

Wyoming

-59

-116

-173

210

140

Quartile 3

Arizona

-36

-21

-77

-85

34

Georgia

6

52

-103

221

-31

Indiana

-97

48

-44

55

-61

Iowa

-3

-6

56

90

-7

Maine

32

128

96

-156

-16

Missouri

-34

-50

-93

-16

-68

Nebraska

-34

-43

24

66

75

North Caroline

-20

-61

-49

52

-27

North Dakota

-92

37

61

-134

47

Oklahoma

-48

-3

-37

37

-32

Tennessee

-101

8

-35

72

-7

Texas

-52

-43

-122

35

-33

Vermont

39

-98

52

-197

30

Quartile 4

Alabama

-71

12

-117

181

-24

Arkansas

-129

37

-40

-10

-53

Idaho

-85

-68

-58

-3

-23

Kentucky

-78

85

17

-87

-32

Louisiana

-125

-39

-33

153

-15

Mississippi

-169

30

-37

172

-23

Montana

-92

-116

-21

-145

36

New Mexico

-52

-98

-5

-7

43

South Carolina

-113

15

-33

137

-17

South Dakota

-59

-68

-54

-125

16

Utah

-31

-83

-58

-81

68

West Virginia

-111

41

-21

-68

-17

When these estimated state effects are analyzed, they show that state fiscal capacity interacts with program area (i.e., the relationship with fiscal capacity varies with program area). Exhibit III-14 shows these variations by displaying the average state effects, in their standardized versions, for states of different fiscal capacities, using our basic four quartiles. The relationship between state effects and fiscal capacity are compared across four different program areas: cash assistance, Medicaid, non-health social services, and public hospitals. We should note that the differences in state effects are most important, not the absolute values (e.g., whether they are negative or positive, that is, above or below the average state effects across all states).

Exhibit III-14 indicates that states of different fiscal capacities still vary in their long-run spending patterns even after controlling for the linear effects of annual changes in states' per capita personal income, as the 50-state model does. For example, the wealthiest states (Quartile 1) spent on average about $180 more per capita per year on cash assistance than did the poorest quartile (Quartile 4). A consistent and positive, albeit weaker, relationship between fiscal capacity and average state effects is also evident in spending on non-health social services.

Exhibit III-14.
Average State Effects for Different Types of Social Welfare Spending, by State Fiscal Capacity, Based on Data From 1977-2000

Health-related expenditures show a different pattern. With respect to Medicaid, the average state effects for the richest states were higher than for states in the other quartiles, but the differences among the three less wealthy quartiles were small. The relationship between fiscal capacity and spending on public hospitals was actually reversed. Per capita spending was lowest among the richest states and highest among the poorest states. After controlling for the linear effects of annual changes in fiscal capacity and other variables, as the 50-state model does, poor states still spent less on cash assistance and other social welfare, while their spending on health-related programs was not much lower and sometimes higher than the amount wealthier states spent.

Poor states, on average, thus revealed greater support for spending on health-related programs than for spending on non-health programs. One possible consequence of this pattern was a weaker statistical relationship among poor states in their support across different program areas. Among non-poor states (i.e., states in the first three quartiles for fiscal capacity), tendencies to spend on different social welfare functions were, for the most part, either positively correlated with each other or not correlated at all, suggesting that no major tradeoff existed among these states between their financial support for one type of social welfare and their support for another.

We can see these relationships in the first column of Exhibit III-15, which shows the bivariate correlation coefficients between the state effect estimates for cash assistance, Medicaid, non-health social services, and public hospitals. For the 38 states in the first three quartiles of fiscal capacity, the correlations were generally either positive or especially small. The strongest correlation was between Medicaid and non-health social services, though a moderate relationship also existed between cash assistance and non-health social services. Only the state effects for public hospitals showed a slight negative relationship to state effects for other types of spending.

Exhibit III-15.
Correlations Between State Effects for Different Types of Social Welfare Spending

Types of Spending

Pearson correlations between estimated state effects for
different types of spending, by state fiscal capacity

Non-poor States

Poor States

Cash Assistance vs. Non-health Social Services

.33

-.15

Cash Assistance vs. Medicaid

-.01

-.51

Cash Assistance vs. Public Hospitals

-.23

-.51

Non-health Social Services vs. Medicaid

.50

.13

Non-health Social Services vs. Public Hospitals

-.22

-.40

Medicaid vs. Public Hospitals

.17

.33

Number of cases

38

12

By contrast, among the 12 poorest states, the correlations among these spending tendencies were more likely to be negative. Cash assistance was negatively correlated with both types of health-related functions, Medicaid and public hospitals. Non-health social services was also negatively related to spending on public hospitals and, albeit weakly, cash assistance. On the other hand, the poor states showed a slightly stronger relationship between the two types of health program areas. We can see an example of the contrasting structure of these relationships in Exhibit III-16, which shows the scatterplots between the state effects for cash assistance and Medicaid-separately for poor and non-poor states. No correlation existed between the estimated state effects for non-poor states, but a clear negative relationship existed among the poor states.

Exhibit III-16.
Scatterplots Between State Effects for Payments to Medicaid and Cash Assistance, Based on Model Estimated for Years 1977-2000

Scatterplot between state effects estimated for Medicaid and cash assistance, only states in Quartiles 1, 2, and 3 in fiscal capacity (i.e., wealthier 75%)

Scatterplot between state effects estimated for Medicaid and cash assistance, only states in Quartile 4 in fiscal capacity (plus Arizona, because it is one of the study states and is near the cutoff point between Quartiles 3 and 4)

More generally, low fiscal capacity states divided between those that put money into health programs and little else and those that put money into other programs, especially cash assistance. As Exhibit III-16 shows, the former were southern and border states, including Mississippi, Arkansas, West Virginia, and South Carolina. Poor western states, including Utah and New Mexico, showed greater levels of support for cash assistance. Whatever the reasons for these differences among poor states, such states clearly showed divisions in their spending patterns across different functions. Poor states, unlike wealthy states, seemed to choose or specialize in one or another type of social program area. Their packages of social programs were, thus, more particularized as well as smaller. Although knowing how much a wealthy state spent in one social program area often helped us know how much it spent in another area, the same was untrue for poor states.

Although per capita income generally had the expected positive effect on spending, notable differences occurred between rich and poor states. When we analyzed the sample separately by quartile, we found the income effects on cash assistance, non-health social services, and public hospitals much more consistently larger and statistically significant for the rich states than for the poorer states. On the other hand, the income effects on Medicaid were larger and more positive for the poorer states than for the richer states. This finding suggests that when personal income rises in the richer states, the states are more likely to increase social welfare spending across the board, and when income rises in the poorer states, spending is likely to occur largely on Medicaid.

ii) Effects of Federal Grants

Although federal grants largely increased state and local spending on social welfare, the effects on federal grants were hardly noticeable for the poorest states (Quartile 4), except for a positive effect on Medicaid. The grant effects were most apparent on payments to Medicaid, suggesting the importance of the Medicaid matching funds.

iii) Effects of Need Variables, Including Unemployment

Estimating a stable needs function that would predict well state and local spending proved impossible. That poverty seemed negatively correlated with spending in a number of spending categories was puzzling, particularly for the richest states. Although the sign on the per capita unemployment was much more likely to be positive than the sign on the poverty variable, the statistically significant positive unemployment effects on spending seemed generally confined to the richer states. The strongest positive effects of unemployment occurred on cash assistance spending. This result might constitute a kind of caseload effect, but it fails to occur in Quartile 4 for the poorest states. The effects of population density on social welfare spending were generally mixed, but we estimated a number of coefficients to be statistically significant.

The poorer states seem to have less protection against adverse unemployment effects, and their needs are more likely to go unmet in a downturn. When we more closely evaluated the effect of state unemployment on spending using the state unemployment rate, we found that cash assistance and Medicaid spending were positively related to the unemployment rate with no income control, particularly for the richer states. However, for non-health social services, the coefficient on unemployment was consistently negative and statistically significant across quartiles and largely statistically insignificant for public hospital spending. We conclude that the total effect of a rise in unemployment is likely to be a cutback in spending for non-health social services across all states with increases in spending for cash assistance and Medicaid in richer states.

iv) State Effects

Stable differences among states in their spending patterns persisted even after controlling for the linear effects of fiscal capacity, need, federal grant, and other independent variables. These propensities to spend (i.e., estimated state effects) suggested that state fiscal capacity was more strongly related to non-health expenditures than to health-related expenditures. They also suggested that the basic structure of expenditures was different in rich and poor states. In wealthier states, spending on each social welfare function was more likely to be positively related or largely independent of spending on other social welfare functions. In the poorest states, however, spending on each social welfare function, such as Medicaid, was more likely to be negatively related to spending on other functions, such as cash assistance. These negative relationships between expenditures by poor states result in some interesting differences among the states with respect to their spending patterns, one difference being the regional split between western and southern states in their relative emphasis on cash assistance and Medicaid. This is discussed further in the next section.

In sum, the multivariate econometric analyses suggested the following:

Unemployment pushed up spending on cash assistance and Medicaid but not on non-health service spending.

Growth in state per capita incomes enhanced spending on Medicaid and non-health social services but not necessarily on cash assistance.

Rural states spent less of their money on cash assistance programs and more on health and non-health social services.

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